1. Field of the Invention
The present invention relates to a method correcting for beam hardening in a CT (computed tomography) image, which is composed of pixels arranged in a matrix, of the type wherein correction data are obtained from an initial CT image by re-projecting the pixel from the initial image at a large number of projection angles, with pixels from the initial image being compared with a threshold value for each of the projection angles during the re-projection, and the correction data are used to determine a corrected image from the initial image.
2. Description of the Prior Art
A method of this above type is disclosed, for example, in U.S. Pat. Nos. 6,035,012 and 4,217,641.
Because of the spectral dependence of the beam attenuation behavior of real bodies in the case of polychromatic X-rays a shift in the average energy of the X-rays emerging from an irradiated body toward higher energy values occurs. This effect is referred to as beam hardening. In the reconstructed image of the body, this effect is manifested as deviations in the gray-scale value as compared with the theoretical case of linear, spectrally independent beam attenuation. The gray-scale value deviationsxe2x80x94or beam hardening artefactsxe2x80x94caused in particular by materials with a high atomic number and density (for example bones) in the reconstructed image interfere with the diagnostic content of the image and, in the worst case, can lead the investigating physician to misinterpretation. The beam hardening correction is carried out in order to eliminate these artefacts, at least to some extent.
In known methods of the type initially mentioned, the procedure operates such that, for the individual projection angle and before the re-projection, those pixels which lie below the threshold value are set to zero before the re-projection of the entire pixel matrix is carried out.
For the re-projection, substantially two methods are considered:
The complete integral transformation of the image reconstruction of the initial image is made reversible (see U.S. Pat. No. 4,616,318). In particular, effects which are caused by the reconstruction core, such as cupping correction and so on, can be corrected in this way. The complexity of inverse Fourier reconstruction methods is very high, so that an application in real time is not readily possible in practice.
Starting from the pixel matrix of the initial image, the corresponding parallel projections are determined directly by approximate calculation of the linear integral. Ray-tracing algorithms fall into two classes: (a) pixel-intercepting methods and (b) forward-projection methods (FPM). Both methods are pixel-driven in the sense that no projection beams are specified, but instead the pixel co-ordinates are the starting point for the assessment of contributions to the attenuation. In this way, the influence of the reconstruction kernel cannot be taken into account. In the case of kernels without a cupping correction being used, however, this proves to be unnecessary for the first image reconstruction.
In the following, the procedure in the FPM described in T. M. Peters, xe2x80x9cAlgorithms for fast back- and re-projection in computed tomographyxe2x80x9d IEEE Trans. Nucl. Sci., vol. NS-28, pp. 3641-3647, 1981, is outlined as an example of a pixel-oriented algorithm.
Let the starting point be an initial image having Nxc3x97N square pixels. If b is the edge length of a pixel, then the result for the coordinates of the center of the pixel (n,nxe2x80x2) in a rectangular coordinate system having the axes x and y is
xn=nb, ynxe2x80x2=nxe2x80x2b.
A predefined set of parallel beams is defined by the angle xcex8 with respect to a fixedly chosen reference axis, for example the y axis. The distance of the pixel (n,nxe2x80x2) from the origin (=pixel (0,0)) is therefore given by
t=xn cos xcex8+ynxe2x80x2, cosxcex8.
If a is the distance of the parallel beams from one another, then the selected pixel (n,nxe2x80x2) is consequently located between the beams K and K+1, it being true that
Kxe2x89xa6t/a less than K+1.
In order to decide the manner in which the pixel value Pn,nxe2x80x2 contributes to the attenuation integral, the weighting factor
aK=t/axe2x88x92K(0xe2x89xa6aK less than 1)
is calculated, and the contribution to the adjacent beams is given as
S(K)xe2x86x92S(K)+(1xe2x88x92aK)Pn,nxe2x80x2,
S(K+1)xe2x86x92S(K+1)+aKPn,nxe2x80x2.
It is obvious that the number of beams plays no part in the complexity of the algorithm. If Np is the number of projections of the parallel data, then the run time of a complete image reconstruction is on the order of Npxc2x7N2.
For a practical application of FPM in the course of a beam hardening correction, the run time primarily plays a significant part. A first starting point for optimizing the run time is to reduce the size of the image matrix, which corresponds to a reduction in the maximum frequency contained in the image. This leads to xe2x80x9cfadingxe2x80x9d of the contrast, which is tolerable only within certain limits, since the accuracy of the determined bone thickness in the correction method does not necessary have to be on the order of magnitude of the pixel size in order to achieve usable results. In the event of linear shrinkage of the image size by the factor c, the computing outlay is reduced by the factor c2, because of the orientation of the pixels.
General measures which can lead to a reduction in the computing time are described in the article by Dieberger, A.: Optimierung an der Quelle [optimization at the source], part 3, c""t, volume 3, 1991, pp. 302-312.
An object of the present invention is to provide a method of the type initially described wherein a reduction in the run time is also possible without any reduction in the size of the image matrix.
According to the invention, this object is achieved by a method of correcting for beam hardening for an initial CT image, which is composed of pixels arranged in a matrix, having the following method steps,
correction data are determined from the initial image by re-projecting the pixels from the initial image at a large number of projection angles, the pixels from the initial image being compared with a threshold value for each of the projection angles during the re-projection, and the re-projection being carried out only for those pixels from the initial image whose pixel value lies above the threshold value, and
the correction data are used to determine a corrected image from the initial image.
The invention makes use of the fact that, to decrease the attenuation contribution resulting from hardening materials, only the pixels from the image which lie above the threshold value, those pixels whose pixel value (CT number) lies above a threshold value that is critical for the respective material, are relevant. In the case of bones, for the case in which a beam hardening correction is desired, for example in the area of the base of the skull, experience shows that these are less than 20% of the pixel from the initial image.
It is therefore sufficient, according to the invention, when determining correction data to include only those pixels from the initial image in the re-projection, whose pixel value lies above the threshold value, i.e., to carry out the re-projection only for those pixels.
Because of the reduction in the number of pixels to be taken into account, this permits time optimization of the re-projection operation without reducing the quality of the data produced, in particular the parallel data.
In a first embodiment of the invention, for each of the projection angles during the re-projection, those pixels on the initial image are determined whose pixel value lies above the threshold value.
In this case, given linear indexing of the image matrix, the index of the loops to be executed for the respective projection runs from 1 to N2. Since, for each pixel, it is directly determined whether its pixel value lies above the threshold value, the actually time-consuming steps such as the reconstruction of the two-dimensional co-ordinates of the pixel have to be carried out only for those pixels whose pixel value lies above the threshold value. If a is the proportion of the pixels that contributes to a projection, i.e., that lie above the threshold value, as compared with the number of all the pixels in the initial image, then an acceleration by the factor xcex1xe2x88x921 occurs with respect to the time-consuming steps. Because of the loop overhead, (the run time which is needed in order to determine the pixels whose pixel value lies below the threshold value), this theoretically possible acceleration is, however, not achieved overall.
In a further embodiment of the invention, before the re-projection of the initial image, those pixels from the initial image are determined and saved whose pixel value lies above the threshold value, and for each of the projection angles, these saved pixels lying above the threshold value are used for the purpose of re-projection. Thus, a speed-up does occur, which comes very close to the theoretically possible factor of xcex1xe2x88x921, since, in addition to the run time necessary for the reconstruction of the relevant pixels, (those lying above the threshold value), the run time which additionally arises is only that which is needed to determine the relevant pixels once. The actual loop for the re-projection for each projection angle runs through an index from 1 to xcex1xc2x7N. In practice, the acceleration can be even greater than xcex1xe2x88x921, for example because of accesses to the cache memory of the electronic computing device carrying out the described operations.
In this case, in a preferred embodiment of the invention, the pixels from the initial image whose pixel value lies above the threshold value are saved in a data set which, for each pixel lying above the threshold value, contains the two-dimensional co-ordinates of the center of the pixel and the associated pixel value. As compared with the possible saving of the relevant pixels in a data set which contains the linear index and the pixel value, which is also possible according to an embodiment of the invention, this embodiment offers the run-time advantage that the two-dimensional co-ordinates of the relevant pixels needed for the re-projection have to be calculated only once.